I have tried about every combination of things to keep my hands warm in the brutal cold of ND. When the temps are 0 or slightly above, I typically wear a light liner glove and a heavier type mitt/chopper of some type. I take the mitt off my shooting hand and typically keep the shooting hand in my pocket to stay warm.
When the temp is below 0, which is a lot of time during the winter in ND, I have electric hand warmers in both pockets. They last about 4 hours, so I have 4 or so ready to go to last an entire day/night of hunting and swap them out when they aren't warm any longer. I will keep my hands in the mitts until ready to start calling and then I will take off the mitt on my shooting hand and put it in my pocket to stay warm and ready to pull the trigger.